Complex Problems: The Multiplication of Doubt

In my last two posts which build the foundation of my epistemological framework, I have described how the complexity of problems can be defined through building a hierarchy of constructs and relationships in the order of their complexity. There, I briefly describe the most basic elements with a rudimentary explanation for its complexity ranking as a standalone element. To follow, I described the most basic element, existence, and the general concept of abstraction, which allows us to discuss doubt as a concept which is the abstraction of certainty.

Let us build on the previous discussion here of the nature of knowledge as being inherently probabilistic. Let the certainty of the truth of any given proposition X be represented as Pr(X) in standard statistical notation. Suppose X is some basic proposition with the lowest level of complexity: "The spoon exists," for example, where a spoon is observed on a table in front of you. Having experienced the spoon in front of you, and indeed, currently experiencing it in front of you, you would have supreme confidence in the existence of the spoon. You could not provide a logical proof of the spoon's existence, but you could say that you are as close to absolute certainty in this proposition as one may be; in other words, the limit of Pr(X) approaches 1 in this case. For ease of demonstration, let's suppose Pr(X) = 0.9999.

Determinism, Laplace's Demon, and the Statistical Divide

The concept of ex post determinism, which I have referred to here as scientific determinism, is not a new concept by any stretch. Various forms of determinism have been proposed and debated over the last several centuries, and while the boundaries I have laid out may differ, the idea that events are deterministic is well trodden ground.

Perhaps one of the most extreme, or pure, forms of determinism is represented by Laplace's demon. "Laplace's demon" is the name given to the ideas posited in a passage late in Laplace's life on probability (available here). In simple terms, Laplace expressed the idea of pure determinism: If the position and speed of all particles in the universe are known at a time t=0, then the state of the world at a later time t=1 can be perfectly calculated. Laplace, an early statistician, perhaps most clearly demonstrates the divide between frequentist (or probabilist) and Bayesian modes of thought: You may notice that Laplace's demon seems to have nothing at all to do with statistics as we know it today.